In a communication system and a service, for example, digital video broadcasting (DVB), an asymmetric digital subscriber line (ADSL), a very high-data rate digital subscriber line (VDSL), WiMax, Wi-Fi, or the like, forward error correction (FEC) is a technology for data packet erasures control in data transmission via an unreliably or nosy communication channel. In the FEC technique, a transmitter encodes a data packet in a redundant way using an FEC code. Redundant data (such as a parity bit) allows a receiver to often detect a limited number of erasure data among transmission data packet in order to recover an erased data packet without retransmission. The FEC provides an ability capable of recovering an erased data packet without a reverse channel for requesting retransmission of a data packet to a receiver, but requires fixed and high forward channel bandwidth costs. Also, the FEC is applied under a circumstance where retransmission is expensive or impossible when a data packet is transmitted to a plurality of users during a multi-cast mode.
Conventionally, to solve this problem, a method of using a lookup table before encoding and decoding operations has been used, but this lookup table setting is used for a mathematical operation in a Galois Field, and using a lookup table for the mathematical operation may slow down the speed of encoding and decoding processes. Also, a multiblock FEC scheme uses a generation matrix (G) which is a Cauchy matrix form, but a Cauchy matrix form of a generation matrix determined in advance reduces power of the FEC scheme due to repetition of redundant data (symbol) in the multiblock FEC scheme. Also, in case of calculating an inverse matrix of a generation matrix and decoding an original message from an encoded message, a procedure designed for calculating an inverse matrix of a generation matrix (determinant calculation, vector multiplication, and elements addition) is complicated and a time consumed in a data decoding step may increase.